Question

in any series the term of n is 3-2 n. so find sum of n term​

Answer 1

Answer:

First term (a) = 3 - 2×(1) = 1

a2 = 3 - 2×(2) = -1

a3 = 3 - 2×(3) = -3

As the difference between a3,a2 and a2,a1 is same so the series is in AP

common difference (d)= -1 - 1 = -2

$sum \: = \frac{n}{2} (2a + (n - 1)d) \\ = \frac{n}{2} (2 + (n - 1)( - 2)) \\ = \frac{n}{2} (2 - 2n + 2) \\ = \frac{n}{2} (4 - 2n) \\ = n(2 - n) \\ = 2n - {n}^{2}$

which is the required ans